Certain friction characteristics in aircraft landing gear brakes can lead to fore-and-aft oscillations of the landing gear called "gear walk." These friction characteristics are frequently associated with a particular type of brake lining. Historically, this brake lining friction characteristic has been called "negative damping," since it effectively feeds energy into the landing gear system. Negative damping is mathematically defined as an increase in brake friction that is proportional to a decrease in brake lining rubbing speed. As the aircraft slows to a stop, the brakes become grabby and torque increases without having received an increase in brake pedal pressure. This change in torque can cause divergent oscillations of the landing gear in the fore-and-aft direction, such as those shown in FIG. 1. The vibrations are initially small but become larger with each oscillation until some peak amplitude A is reached as shown in FIG. 1.
Gear walk is generally an undesirable characteristic, due to the loads that can be imposed by the oscillations of the landing gear components. In addition, the resultant aircraft motion during braking may be disconcerting to passengers and crew.
Currently, it is known that a tuned mass absorber can be employed to address a forced steady state vibration problem where attenuation of vibration of some object is desired. The classic application is to apply a tuned mass absorber to a second order mass spring damper-type assembly that is being excited by an external sinusoidal force. A tuned mass absorber is attached to the assembly and is sized and tuned using a steady state analytical solution to the problem. This results in the peak amplitude assembly motions being greatly attenuated. The classic tuned mass absorber application can be demonstrated in the following simplified example. Referring to FIG. 2, an object O with mass M.sub.1 is moved relative to ground through a spring S.sub.1 having a spring constant K.sub.1. The object O is subjected to a force Fsin(.omega.t) which results in vibration of the object O. The force cannot simply be eliminated due to some unspecified reason. The goal is therefore to reduce the vibration of the object O by some other means.
One method of achieving this goal is to employ a tuned mass vibration absorber. This is represented in FIG. 2 as an absorber mass M.sub.2 attached to a spring S.sub.2 having a spring constant K.sub.2. The spring S.sub.2 is further attached to the object mass M.sub.1. The mass M.sub.2 is allowed to move. If mass M.sub.2 and spring S.sub.2 are properly tuned, then the motion of the mass M.sub.2 will exert a force on mass M.sub.1 that is equal and opposite to the force already acting on the object O. The result is a cancellation of forces, with the object O remaining at rest while the absorber mass M.sub.2 moves in a sacrificial manner. The design of a tuned mass absorber requires knowledge of the frequency .omega. of the object's motion, the magnitude of the sinusoidal force F acting on the object, and either the maximum allowable size of the absorber mass M.sub.2 or its maximum allowable range of motion X.sub.2. The following equation describes the relationship between these variables. EQU F=-k.sub.2.times.X.sub.2 =-.omega..sup.2.times.M.sub.2.times.X.sub.2 (1)
Using data from a recent case of gear walk as an example, calculation of the equivalent force F required to move the landing gear at the peak vibration amplitudes observed was as high as 2330 pounds. The landing gear motion occurred at a natural frequency of 9.7 Hz. With a space constraint of 3.1 inches of allowable peak to peak motion, then equation (1) indicates that a mass M.sub.2 of about 150 lbm is required to produce a counterbalancing motion for amplitude A.
It is clear that using the classical design methodology, a rather heavy tuned mass absorber is required to reduce the undesired landing gear motion. This is an impractical solution for aircraft due to the weight penalty, and the fact that landing gear retraction actuators would not be sized for this additional load. Thus, a need exists for eliminating gear walk in a manner that does not add large amounts of weight to the aircraft and that does not require large amounts of space. The present invention is directed to fulfilling this need.